W.L. 14/11/09 Math 7B
The Big Idea Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
essential Question: What methods are there for comparing things?
3.1 Mixing Juice
A.Q: Which recipe will make juice that is the most “orangey”? Explain your answer.
A:Mix A will make the most “orangey” juice because if you make all of them into a part to whole relation this is the biggest: Mix A = 2 to 5 > Mix D = 3 to 8 > Mix C = 4 to 12 > Mix B = 1 to 5 or concentrate as percentage of mixture: Mix A = 40% > Mix D = 37.5% > Mix C = 33.33% > Mix B = 20%.
B.Q: Which recipe will make juice that is the least “orangey”? Explain your answer.
A:Mix B because Mix B= 1/4= 0.25 (0.25 cups of concentrate per one cup of water) < Mix C = 4/18 = 0.5 < Mix D = 3/6 = 0.6 < Mix A = 2/3 = 0.66. So Mix B is the least “orangey”.
C.Q: Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer. A:240*(½) = 120 (for 240 campers you will need 120 cups of juice) Mix A:0.4 * 120 = 48 cups of concentrate and 0.6 * 120 = 72 cups of water Mix B:0.2 * 120 = 24 cups of concentrate and 0.8 * 120 = 96 cups of water Mix C:0.33 * 120 = 40 cups of concentrate and 0.67 * 120 = 80 cups of water Mix D:0.375 * 120 = 45 cups of concentrate and 0.625 * 120 = 75 cups of water
Follow Up
1.Q: How did you use ratios in solving Problem 3.1?
A: I used ratios and then said which on is greater than the other to show my thinking and then used the ratios to make percentages.
2.Q: For each recipe, how much concentrate and how much water is needed to
make 1 cup of juice
A: Mix A you need 0.4 concentrate and 0.6 water
Mix B you need 0.2 concentrate and 0.8 water
Mix C you need 0.33 concentrate and 0.67 water
Mix D you need 0.375 concentrate and 0.625 water
W.L.
14/11/09
Math 7B
The Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
essential Question:
What methods are there for comparing things?
3.1 Mixing Juice
A. Q: Which recipe will make juice that is the most “orangey”? Explain your answer.
A: Mix A will make the most “orangey” juice because if you make all of them into a part to whole relation this is the biggest: Mix A = 2 to 5 > Mix D = 3 to 8 > Mix C = 4 to 12 > Mix B = 1 to 5 or concentrate as percentage of mixture: Mix A = 40% > Mix D = 37.5% > Mix C = 33.33% > Mix B = 20%.
B. Q: Which recipe will make juice that is the least “orangey”? Explain your answer.
A: Mix B because Mix B= 1/4 = 0.25 (0.25 cups of concentrate per one cup of water) < Mix C = 4/18 = 0.5 < Mix D = 3/6 = 0.6 < Mix A = 2/3 = 0.66. So Mix B is the least “orangey”.
C. Q: Assume that each camper will get ½ cup of juice. For each recipe, how much concentrate and how much water are needed to make juice for 24 campers? Explain your answer.
A: 240*(½) = 120 (for 240 campers you will need 120 cups of juice)
Mix A: 0.4 * 120 = 48 cups of concentrate and 0.6 * 120 = 72 cups of water
Mix B: 0.2 * 120 = 24 cups of concentrate and 0.8 * 120 = 96 cups of water
Mix C: 0.33 * 120 = 40 cups of concentrate and 0.67 * 120 = 80 cups of water
Mix D: 0.375 * 120 = 45 cups of concentrate and 0.625 * 120 = 75 cups of water
Follow Up
1. Q: How did you use ratios in solving Problem 3.1?
A: I used ratios and then said which on is greater than the other to show my thinking and then used the ratios to make percentages.
2. Q: For each recipe, how much concentrate and how much water is needed to
make 1 cup of juice
A: Mix A you need 0.4 concentrate and 0.6 water
Mix B you need 0.2 concentrate and 0.8 water
Mix C you need 0.33 concentrate and 0.67 water
Mix D you need 0.375 concentrate and 0.625 water